Nonnegative minimum biased quadratic estimation in mixed linear models

JOURNAL OF MULTIVARIATE ANALYSIS

卷:80

Article

Gnot, S ; Grzadziel, M

关键词: mixed linear model;    quadratic estimation;    nonnegative minimum biased estimators;    mean squared error;    one-way classification model;    symmetric cone;    primal-dual interior-point method;   

DOI  :  10.1006/jmva.2000.1979

来源: Elsevier

【 摘 要 】

The problem of nonnegative quadratic estimation of a parametric function gamma(beta, sigma) = beta'Fbeta + Sigma(i=1)(r) f(i)sigma(i)(2) in a general mixed linear model M{y, Xbeta, V(sigma) = Sigma(i=1)(r) sigma(i)(2)V(i)} is discussed. Necessary and sufficient conditions are given for y'A(0)y to be a minimum biased estimator for gamma. It is shown how to formulate the problem of finding a nonnegative minimium biased estimator of gamma as a conic optimization problem, which can be efficiently solved using convex optimization techniques. Models with two variance components are considered in detail. Some applications to one-way classification mixed models are given. For these models minimum biased estimators with minimum norms for square of expectation beta(2) and for sigma(1)(2) are presented in explicit forms. (C) 2001 Elsevier Science.

【 授权许可】

Free